Anisotropic resistivity reconstruction with virtual resistive network and Faraday's law.

Abstract

The reconstruction of resistivity tensor algorithm in two space dimension was introduced. The mimetic type discretization provided a virtual resistive networks for anisotropic resistivity body. The Faraday's law was considered, which allowed us the local reconstruction algorithm, and it used a right amount of current densities. The reconstruction algorithm was explicit and local. There were two issues of reconstruction algorithm. The first one was the singularity of coefficient matrix of reconstruction relation. We studied the singular property of the isotropic, orthotropic and anisotropic cases. We resolved the singularity issue using a network structure. The second issue was noise stirpes caused by characteristic lines. The noise stirpes phenomena is an intrinsic property of hyperbolic type problem. To overcome the noise effect we designed a denoising method using a property of the reconstruction algorithm.